P100 GPU Research Articles

AI-Driven Computer Vision Detection of Cotton in Corn Fields Using UAS Remote Sensing Data and Spot-Spray Application

To effectively combat the re-infestation of boll weevils (Anthonomus grandis L.) in cotton fields, it is necessary to address the detection of volunteer cotton (VC) plants (Gossypium hirsutum L.) in rotation crops such as corn (Zea mays L.) and sorghum (Sorghum bicolor L.). The current practice involves manual field scouting at the field edges, which often leads to the oversight of VC plants growing in the middle of fields alongside corn and sorghum. As these VC plants reach the pinhead squaring stage (5–6 leaves), they can become hosts for boll weevil pests. Consequently, it becomes crucial to detect, locate, and accurately spot-spray these plants with appropriate chemicals. This paper focuses on the application of YOLOv5m to detect and locate VC plants during the tasseling (VT) growth stage of cornfields. Our results demonstrate that VC plants can be detected with a mean average precision (mAP) of 79% at an Intersection over Union (IoU) of 50% and a classification accuracy of 78% on images sized 1207 × 923 pixels. The average detection inference speed is 47 frames per second (FPS) on the NVIDIA Tesla P100 GPU-16 GB and 0.4 FPS on the NVIDIA Jetson TX2 GPU, which underscores the relevance and impact of detection speed on the feasibility of real-time applications. Additionally, we show the application of a customized unmanned aircraft system (UAS) for spot-spray applications through simulation based on the developed computer vision (CV) algorithm. This UAS-based approach enables the near-real-time detection and mitigation of VC plants in corn fields, with near-real-time defined as approximately 0.02 s per frame on the NVIDIA Tesla P100 GPU and 2.5 s per frame on the NVIDIA Jetson TX2 GPU, thereby offering an efficient management solution for controlling boll weevil pests.

Rapid Localization of Gravitational Wave Sources from Compact Binary Coalescences Using Deep Learning

The mergers of neutron star–neutron star and neutron star–black hole binaries (NSBHs) are the most promising gravitational wave (GW) events with electromagnetic (EM) counterparts. The rapid detection, localization, and simultaneous multimessenger follow-up of these sources are of primary importance in the upcoming science runs of the LIGO-Virgo-KAGRA Collaboration. While prompt EM counterparts during binary mergers can last less than 2 s, the timescales of existing localization methods that use Bayesian techniques, vary from seconds to days. In this paper, we propose the first deep learning–based approach for rapid and accurate sky localization of all types of binary coalescences, including neutron star–neutron star and NSBHs for the first time. Specifically, we train and test a normalizing flow model on matched-filtering output from GW searches to obtain sky direction posteriors in around 1 s using a single P100 GPU, which is several orders of magnitude faster than full Bayesian techniques.

Deep learning pest detection on Indonesian red chili pepper plant based on fine-tuned YOLOv5

.This research developed a pest detection model for Indonesian red chili pepper based on fine-tuned YOLOv5. Indonesian red chili pepper is the third largest vegetable commodity produced in Indonesia. Pest attacks disrupt the quantity and quality of crop yields. To control pests effectively, it is necessary to detect the type of pest correctly. A viable solution is to leverage computer vision and deep learning technologies. However, no previous studies have developed a pest detection model for Indonesian red chili pepper based on this technology. YOLOv5 is a variant of the YOLO object detection algorithm, which has major advantages in terms of computation cost and execution speed. The dataset comprises 4,994 image files collected from a chili plantation in Bengkulu province, Indonesia, covering 4 different classes and a total of 10,683 pests. The image is 1216 x1216 px with the smallest, largest, and average object dimensions of 2%, 35%, and 4% of the image dimensions. The training model used is fine-tuning YOLOv5s with variations of patience as an early stop parameter of 100, 200, and 300. The evaluation of the trained model is based on train loss, validation loss, and mAP@0.5:0.95, the best-trained model is the 445th epoch on patience 100 with the best confidence value of 0.321 and the highest TF1 of 0.74. From the best-trained model testing on the test dataset, the mAP@0.5 performance for all classes is 81.3%. The model not only detected large pests but was also able to detect objects that were small in size compared to the image size. The best-trained model's best mAP@0.5 performance and speed are 82.6% and 20 ms/image, or 50 fps on NVIDIA P100 GPU.

Improving Performance of VGG-19 Model using Dual Input Block for Skin Disease Classification

Skin diseases are a growing threat to humans. They can cause severe damage to the skin. The damage to the skin sometimes can lead the patient to have a loss of confidence and depression. By using emerging technologies like deep learning, we can identify skin diseases and treat them effectively. These computer-powered techniques can detect skin diseases without any help from a professional. People can have a user-friendly experience if some effort is put into the interface. This can help people identify the disease in its early stages instead of just ignoring it as an allergy. This will help people avoid suffering from the severe consequences of the diseases. By using these technologies, we can accurately find the disease in the patient. By using deep learning algorithms like those at CNN, we can make things simpler and less time-consuming. By using advanced models like Inception Net and ResNet and optimizing the model's hyperparameters like learning rate, optimizers, etc., the model can give high performance and accuracy. The model can be trained to give accurate results even if the images used in the training dataset and the image given by the patient are of low quality. We propose a dual-input CNN model to identify skin diseases. We use a modified VGG-19 neural network with dual input blocks and batch normalization to classify the diseases. The model outperforms the original VGG19 by about 5 percent. The original model, trained from scratch, was also modified to have batch normalization. The models did not learn, and the accuracy did not increase without batch normalization. The models were trained for 150 epochs. Both were trained under the same parameters and methods. The dual input model yields about 94%, while the original VGG19 architecture trained from scratch gives about 89%. The models were trained on P100 GPU are available in Kaggle. The model is implemented on hardware that can give results without any delay to the patient.

Enable high-resolution, real-time ensemble simulation and data assimilation of flood inundation using distributed GPU parallelization

Numerical modeling of the intensity and evolution of flood events are affected by multiple sources of uncertainty such as precipitation and land surface conditions. To quantify and curb these uncertainties, an ensemble-based simulation and data assimilation model for pluvial flood inundation is constructed. The shallow water equation is decoupled in the x and y directions, and the inertial form of the Saint-Venant equation is chosen to realize fast computation. The probability distribution of the input and output factors is described using Monte Carlo samples. Subsequently, a particle filter is incorporated to enable the assimilation of hydrological observations and improve prediction accuracy. To achieve high-resolution, real-time ensemble simulation, heterogeneous computing technologies based on CUDA (compute unified device architecture) and a distributed storage multi-GPU (graphics processing unit) system are used. Multiple optimization skills are employed to ensure the parallel efficiency and scalability of the simulation program. Taking an urban area of Fuzhou, China as an example, a model with a 3-m spatial resolution and 4.0 million units is constructed, and 8 Tesla P100 GPUs are used for the parallel calculation of 96 model instances. Under these settings, the ensemble simulation of a 1-hour hydraulic process takes 2.0 min, which achieves a 2680 × estimated speedup compared with a single-thread run on CPU. The calculation results indicate that the particle filter method effectively constrains simulation uncertainty while providing the confidence intervals of key hydrological elements such as streamflow, submerged area, and submerged water depth. The presented approaches show promising capabilities in handling the uncertainties in flood modeling as well as enhancing prediction efficiency.

Acceleration of Bi-Objective Optimization of Data-Parallel Applications for Performance and Energy on Heterogeneous Hybrid Platforms

Accelerating the bi-objective optimization of applications for performance and energy is crucial to achieving energy efficiency objectives and meeting quality-of-service requirements in modern high-performance computing platforms and cloud computing infrastructures. In this work, we highlight the crucial challenges to accelerate model-based methods proposed for the bi-objective optimization of data-parallel applications for performance and energy that employ workload distribution between the executing processors as the decision variable. The methods solve unconstrained bi-objective optimization problems and take input, the processors’ performance and energy profiles in the form of discrete functions of workload size, and output Pareto-optimal solutions (workload distributions), minimizing the execution time and the total energy consumption of computations during the parallel execution of the application. One of the challenges is the fast computation of Pareto-optimal solutions. We then formulate the bi-objective optimization problem of data-parallel applications for performance and energy through workload distribution on a cluster of p identical hybrid nodes, each containing h heterogeneous processors. The state-of-the-art algorithm for solving the problem is sequential and takes exorbitant execution times to find Pareto-optimal solutions for even moderate numbers of processors. We propose two algorithms that address this shortcoming. The first algorithm is an exact sequential algorithm that is more efficient and amenable to parallelization and achieves a complexity reduction of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (m × h) over the state-of-the-art sequential algorithm where m is the cardinality of the input discrete execution time and dynamic energy functions. The second algorithm is a parallel algorithm executed by q identical parallel processes that reduces the complexity of our proposed sequential algorithm by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (q) and therefore achieves a complexity reduction of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (m×h×q) over the state-of-the-art sequential algorithm. Finally, we experimentally analyze the practical efficacy of our proposed algorithms for two data-parallel applications, matrix multiplication and fast Fourier transform, on a heterogeneous hybrid node containing an Intel Haswell multicore CPU, an Nvidia k40c GPU, and an Nvidia P100 GPU and simulations of clusters of such hybrid nodes. The experiments demonstrate that our proposed algorithms provide tremendous speedups over state-of-the-art solutions.

Strategies to parallelize a finite element mesh truncation technique on multi-core and many-core architectures

Achieving maximum parallel performance on multi-core CPUs and many-core GPUs is a challenging task depending on multiple factors. These include, for example, the number and granularity of the computations or the use of the memories of the devices. In this paper, we assess those factors by evaluating and comparing different parallelizations of the same problem on a multiprocessor containing a CPU with 40 cores and four P100 GPUs with Pascal architecture. We use, as study case, the convolutional operation behind a non-standard finite element mesh truncation technique in the context of open region electromagnetic wave propagation problems. A total of six parallel algorithms implemented using OpenMP and CUDA have been used to carry out the comparison by leveraging the same levels of parallelism on both types of platforms. Three of the algorithms are presented for the first time in this paper, including a multi-GPU method, and two others are improved versions of algorithms previously developed by some of the authors. This paper presents a thorough experimental evaluation of the parallel algorithms on a radar cross-sectional prediction problem. Results show that performance obtained on the GPU clearly overcomes those obtained in the CPU, much more so if we use multiple GPUs to distribute both data and computations. Accelerations close to 30 have been obtained on the CPU, while with the multi-GPU version accelerations larger than 250 have been achieved.

Localization of lung abnormalities on chest X-rays using self-supervised equivariant attention

Chest X-Ray (CXR) images provide most anatomical details and the abnormalities on a 2D plane. Therefore, a 2D view of the 3D anatomy is sometimes sufficient for the initial diagnosis. However, close to fourteen commonly occurring diseases are sometimes difficult to identify by visually inspecting the images. Therefore, there is a drift toward developing computer-aided assistive systems to help radiologists. This paper proposes a deep learning model for the classification and localization of chest diseases by using image-level annotations. The model consists of a modified Resnet50 backbone for extracting feature corpus from the images, a classifier, and a pixel correlation module (PCM). During PCM training, the network is a weight-shared siamese architecture where the first branch applies the affine transform to the image before feeding to the network, while the second applies the same transform to the network output. The method was evaluated on CXR from the clinical center in the ratio of 70:20 for training and testing. The model was developed and tested using the cloud computing platform Google Colaboratory (NVidia Tesla P100 GPU, 16 GB of RAM). A radiologist subjectively validated the results. Our model trained with the configurations mentioned in this paper outperformed benchmark results.

A Framework for Neural Network Architecture and Compile Co-optimization

The efficiency of deep neural network (DNN) solutions on real hardware devices are mainly decided by the DNN architecture and the compiler-level scheduling strategy on the hardware. When we try to fully exploit the underlying hardware and obtain the optimal tradeoff between DNN accuracy and runtime performance, we discovered that the two optimization goals of DNN architecture and scheduling policy are intimately related to each other. However, current hardware-aware Neural Architecture Search (NAS) methods primarily focus on the DNN architecture search process, ignoring the effects of various compiler-level scheduling strategies (e.g., graph-level optimization, loop transformations, parallelization, etc.) on network candidates being evaluated in the search process. As a result, they may overlook the true-optimal DNN implementations on hardware, which can only be discovered by trying-out different combinations of scheduling strategies and DNN architectures. This work proposes a NAS framework (CHaNAS) that searches for not only the network architecture but also the dedicated compiler-level scheduling policy, as the optimal co-design solution on the target hardware. We propose to use a block-based pre-scheduling methodology to reduce the co-design search space and enable the automatic generation of the optimal co-design, including the network architecture and the tensor programs that practice the scheduling policy. Further, we introduce a new search objective function based on the generalization gap to prevent the selection of architectures that are prone to overfitting. We evaluate CHaNAS on Imagenet on different hardware back-ends against the state-of-the-art hardware-aware search method based on the MobileNet-v3 search space. Experimental results show that the co-design solutions obtained by ChaNAS show up to 1.6×, 1.9×, and 1.7×, 24 performance boost on NVIDIA P100 GPU, Intel Xeon 8163 CPU, and Samsung Note 10 Mobile, respectively, over the baselines of the same-level accuracy.

Customized Deep Learning Classifier for Detection of Acute Lymphoblastic Leukemia Using Blood Smear Images.

Acute lymphoblastic leukemia (ALL) is a rare type of blood cancer caused due to the overproduction of lymphocytes by the bone marrow in the human body. It is one of the common types of cancer in children, which has a fair chance of being cured. However, this may even occur in adults, and the chances of a cure are slim if diagnosed at a later stage. To aid in the early detection of this deadly disease, an intelligent method to screen the white blood cells is proposed in this study. The proposed intelligent deep learning algorithm uses the microscopic images of blood smears as the input data. This algorithm is implemented with a convolutional neural network (CNN) to predict the leukemic cells from the healthy blood cells. The custom ALLNET model was trained and tested using the microscopic images available as open-source data. The model training was carried out on Google Collaboratory using the Nvidia Tesla P-100 GPU method. Maximum accuracy of 95.54%, specificity of 95.81%, sensitivity of 95.91%, F1-score of 95.43%, and precision of 96% were obtained by this accurate classifier. The proposed technique may be used during the pre-screening to detect the leukemia cells during complete blood count (CBC) and peripheral blood tests.

Critique of “MemXCT: Memory-Centric X-Ray CT Reconstruction With Massive Parallelization” by SCC Team From the University of Texas at Austin

This report describes The University of Texas Student Cluster Competition team's effort to reproduce the results of "MemXCT: memory-centric X-ray CT reconstruction with massive parallelization" \cite{memxct}. The paper details a new memory-centric approach that reconstructs X-ray computed tomography (XCT) from noisy raw data. In our reproduction experiments, we utilized Microsoft Azure's CycleCloud tool to provision, orchestrate, and manage our computing cluster in the cloud. In particular, we scheduled and benchmarked reconstruction workloads using Azure's CPU-based HC44rs and GPU-based NC12s v2 virtual machine (VM) types to evaluate the scalability properties of the reconstruction approach and the performance differences between architectures. The HC44rs VMs contained 44 Intel Xeon Platinum cores, while the NC12s v2 VM was equipped with two NVIDIA P100 GPUs. We used a recent version of Intel's compiler stack with the MKL library for our CPU code along with CUDA 11.1 on GPUs. Overall, our results confirm the findings of the original paper, demonstrating similar acceleration on GPUs and scalability properties on CPUs.

FARNN: FPGA-GPU Hybrid Acceleration Platform for Recurrent Neural Networks

GPU-based platforms provide high computation throughput for large mini-batch deep neural network computations. However, a large batch size may not be ideal for some situations, such as aiming at low latency, training on edge/mobile devices, partial retraining for personalization, and having irregular input sequence lengths. GPU performance suffers from low utilization especially for small-batch recurrent neural network (RNN) applications where sequential computations are required. In this article, we propose a hybrid architecture, called FARNN, which combines a GPU and an FPGA to accelerate RNN computation for small batch sizes. After separating RNN computations into GPU-efficient and GPU-inefficient tasks, we design special FPGA computation units that accelerate the GPU-inefficient RNN tasks. FARNN off-loads the GPU-inefficient tasks to the FPGA. We evaluate FARNN with synthetic RNN layers of various configurations on the Xilinx UltraScale+ FPGA and the NVIDIA P100 GPU in addition to evaluating it with real RNN applications. The evaluation result indicates that FARNN outperforms the P100 GPU platform for RNN training by up to 4.2 <inline-formula><tex-math notation="LaTeX">$\times {}$</tex-math></inline-formula> with small batch sizes, long input sequences, and many RNN cells per layer.

FgSpMSpV: A Fine-grained Parallel SpMSpV Framework on HPC Platforms

Sparse matrix-sparse vector (SpMSpV) multiplication is one of the fundamental and important operations in many high-performance scientific and engineering applications. The inherent irregularity and poor data locality lead to two main challenges to scaling SpMSpV over high-performance computing (HPC) systems: (i) a large amount of redundant data limits the utilization of bandwidth and parallel resources; (ii) the irregular access pattern limits the exploitation of computing resources. This paper proposes a fine-grained parallel SpMSpV (fgSpMSpV) framework on Sunway TaihuLight supercomputer to alleviate the challenges for large-scale real-world applications. First,fgSpMSpVadopts an MPI\( + \)OpenMP\( +X \)parallelization model to exploit the multi-stage and hybrid parallelism of heterogeneous HPC architectures and accelerate both pre-/post-processing and main SpMSpV computation. Second,fgSpMSpVutilizes an adaptive parallel execution to reduce the pre-processing, adapt to the parallelism and memory hierarchy of the Sunway system, while still tame redundant and random memory accesses in SpMSpV, including a set of techniques like the fine-grained partitioner, re-collection method, and Compressed Sparse Column Vector (CSCV) matrix format. Third,fgSpMSpVuses several optimization techniques to further utilize the computing resources.fgSpMSpVon the Sunway TaihuLight gains a noticeable performance improvement from the key optimization techniques with various sparsity of the input. Additionally,fgSpMSpVis implemented on an NVIDIA Tesal P100 GPU and applied to the breath-first-search (BFS) application.fgSpMSpVon a P100 GPU obtains the speedup of up to\( 134.38\times \)over the state-of-the-art SpMSpV algorithms, and the BFS application usingfgSpMSpVachieves the speedup of up to\( 21.68\times \)over the state-of-the-arts.

Tea Chrysanthemum Detection by Leveraging Generative Adversarial Networks and Edge Computing.

A high resolution dataset is one of the prerequisites for tea chrysanthemum detection with deep learning algorithms. This is crucial for further developing a selective chrysanthemum harvesting robot. However, generating high resolution datasets of the tea chrysanthemum with complex unstructured environments is a challenge. In this context, we propose a novel tea chrysanthemum – generative adversarial network (TC-GAN) that attempts to deal with this challenge. First, we designed a non-linear mapping network for untangling the features of the underlying code. Then, a customized regularization method was used to provide fine-grained control over the image details. Finally, a gradient diversion design with multi-scale feature extraction capability was adopted to optimize the training process. The proposed TC-GAN was compared with 12 state-of-the-art generative adversarial networks, showing that an optimal average precision (AP) of 90.09% was achieved with the generated images (512 × 512) on the developed TC-YOLO object detection model under the NVIDIA Tesla P100 GPU environment. Moreover, the detection model was deployed into the embedded NVIDIA Jetson TX2 platform with 0.1 s inference time, and this edge computing device could be further developed into a perception system for selective chrysanthemum picking robots in the future.

Hash Functions and GPU Algorithm of Infinite Grid Method for Contact Search

The paper presents the memory-saving GPU algorithm of the infinite grid method with various hash functionsfor contact search in discrete element computations. The implemented hash table of fixed size has the addedbenefit of allowing the grid to be potentially infinite in size, which is particularly suitable for a large numberof discrete particles, moving in large computational domains with empty regions. Research on the applicationof various hash functions and hash table sizes was performed to preserve the computational performance ofthe developed memory-saving GPU algorithm and its OpenCL implementation. The performance of the developed software was evaluated by solving the hopper fill and discharge as well as the artificial avalanche problemson the NVIDIA® Tesla™ P100 GPU. The performance achieved by using the memory-saving implementationof contact search was compared with that attained by using the standard implementation of the uniform gridmethod. The performed analysis revealed that the developed GPU algorithm and its OpenCL implementationreduced the GPU memory consumed by the uniform grid method up to 69.7 times, which resulted in the contactsearch memory equal to 1.86% of the total memory required by DEM computations. Moreover, the applicationof the Morton hash function and the proper hash table size allowed for preserving high computational performance of the infinite grid method and the developed GPU software.

A ResNet-Based Method for Complex Channel Interpretation in Seismic Volumes

Channels usually contribute to the accumulation of reservoirs and their identification is useful in the well placements for mining and oil field development. We consider the task of channel detection as a regression problem and propose a workflow to identify the channels in seismic volumes with complex structures using an end-to-end 3D convolutional neural network. To train the network, we automatically generate a training dataset containing more than 19000 3D synthetic seismic volumes and the corresponding channel labels, which are shown to be sufficient to train our network. Although only trained on the synthetic dataset, the network can automatically learn informative features for channel identification. Multiple synthetic and field applications show that the network can accurately and efficiently separation all the channel reflections in 3D seismic volumes with complex structures. With a NVIDIA P100 GPU, the predicting application takes only 0.6 hours for a 10GB seismic volume with size 1201×1601×1351.

The Performance Analysis of the Thermal Discrete Element Method Computations on the GPU

The paper presents a GPU implementation of the thermal discrete element method (TDEM) and the comparative analysis of its performance. Several discrete element models for granular flows, the bonded particle model and the TDEM are considered for quantitative comparison of computational performance. The performance measured on NVIDIA(R) Tesla™ P100 GPU is compared with that attained by running the same OpenCL code on Intel(R) Xeon™ E5-2630 CPU with 20 cores. The presented GPU implementation of the TDEM increases the computing time of the bonded particle model only up to 30.6 % of the computing time of the simplest DEM model, which is an acceptable decrease in the performance required for solving coupled thermomechanical problems.

Tea chrysanthemum detection under unstructured environments using the TC-YOLO model

Tea chrysanthemum detection at its flowering stage is one of the key components for selective chrysanthemum harvesting robot development. However, it is a challenge to detect flowering chrysanthemums under unstructured field environments given variations on illumination, occlusion and object scale. In this context, we propose a highly fused and lightweight deep learning architecture based on YOLO for tea chrysanthemum detection (TC-YOLO). First, in the backbone component and neck component, the method uses the Cross-Stage Partially Dense network (CSPDenseNet) and the Cross-Stage Partial ResNeXt network (CSPResNeXt) as the main networks, respectively, and embeds custom feature fusion modules to guide the gradient flow. In the final head component, the method combines the recursive feature pyramid (RFP) multiscale fusion reflow structure and the Atrous Spatial Pyramid Pool (ASPP) module with cavity convolution to achieve the detection task. The resulting model was tested on 300 field images using a data enhancement strategy combining flipping and rotation, showing that under the NVIDIA Tesla P100 GPU environment, if the inference speed is 47.23 FPS for each image (416 × 416), TC-YOLO can achieve the average precision (AP) of 92.49% on our own tea chrysanthemum dataset. Through further validation, it was found that overlap had the least effect on tea chrysanthemum detection, and illumination had the greatest effect on tea chrysanthemum detection. In addition, this method (13.6 M) can be deployed on a single mobile GPU, and it could be further developed as a perception system for a selective chrysanthemum harvesting robot in the future.

Detecting spam e-mails using stop word TF-IDF and stemming algorithm with Naïve Bayes classifier on the multicore GPU

&lt;span&gt;A spam filter is a program which is used to identify unwanted emails and prevents those messages from getting into a user's mail. The study was focused on how the algorithms can be applied on a number of e-mails consisting of both ham and spam e-mails. First, the working principle and steps which are followed for implementation of stop words, TF-IDF and stemming algorithm on NVIDIA’s Tesla P100 GPU are discussed and to verify the findings by executing of Naïve Bayes algorithm. After complete training and testing of the spam e-mails dataset taken from Kaggle by using the proposed method, we got a high training accuracy of 99.67% and got a testing accuracy of about 99.03% on the multicore GPU that boosted the speed of execution of training time period and testing time period which is improved of training and testing accuracy around 0.22% and 0.18% respectively when compared to that after applying only Naïve Bayes i.e. conventional method to the same dataset where we found training and testing accuracy to be 99.45% and 98.85% respectively. Also, we found that training time taken on GPU is 1.361 seconds which was about 1.49X faster than that taken on CPU which is 2.029 seconds. And the testing time taken on GPU is 1.978 seconds which was about 1.15X faster than that taken on CPU which is 2.280 seconds.&lt;/span&gt;

FAME

In this article, we propose the Fast Algorithms for Maxwell’s Equations (FAME) package for solving Maxwell’s equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee’s discretization. The GEPs are transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only 0.33 and 3.6 × 10 − 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, in 127 to 191 seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.